美国大学生数学建模 题目 翻译专题_美国数学建模历年题目

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PROBLEM A: The Keep-Right-Except-To-Pa Rule

In countries where driving automobiles on the right is the rule(that is, USA, China and most other countries except for Great Britain, Australia, and some former British colonies), multi-lane freeways often employ a rule that requires drivers to drive in the right-most lane unle they are paing another vehicle, in which case they move one lane to the left, pa, and return to their former travel lane.Build and analyze a mathematical model to analyze the performance of this rule in light and heavy traffic.You may wish to examine tradeoffs between traffic flow and safety, the role of under-or over-posted speed limits(that is, speed limits that are too low or too high), and/or other factors that may not be explicitly called out in this problem statement.Is this rule effective in promoting better traffic flow? If not, suggest and analyze alternatives(to include poibly no rule of this kind at all)that might promote greater traffic flow, safety, and/or other factors that you deem important.In countries where driving automobiles on the left is the norm, argue whether or not your solution can be carried over with a simple change of orientation, or would additional requirements be needed.Lastly, the rule as stated above relies upon human judgment for compliance.If vehicle transportation on the same roadway was fully under the control of an intelligent system – either part of the road network or imbedded in the design of all vehicles using the roadway – to what extent would this change the results of your earlier analysis?

在一些国家在右侧驾驶汽车是一种惯例（比如像美国，中国和其他大部分国家，除了英国，澳大利亚，和一部分之前英国殖民的国家）多车道高速公路普遍建立起这样的规则，那就是要求司机在最右边的车道驾驶汽车，除非他们要超越其它车辆，这种情况下他们要移动到左侧车道，超车，然后回到他们原先的车道。

建立和总结一个数学模型去分析这一规则在流畅和拥堵情况下的交通性能，你不妨检查交通流量和安全，过少或过多限速的作用（即，过低或过高的车速限制）和/或不能在问题陈述中被清楚表达的其它因素。这种规则是否能有效的促进交通流量的提升？如果不是，给出建议并分析取而代之的方法（包括当前没有的规则），此方法会促进更多的交通流量，安全性，和/或包括您认为重要的其他因素。

在一些国家，汽车行驶在左边是常态，阐述您的解决方案是否能可行如果仅仅在方向上作出改变，或者是需要额外的要求。

最后，如上所述的规则依赖于人的判断为标准。如果在相同的道路运输车辆的完全是一个智能系统的控制下，系统要么是在部分的道路网络中，要么是嵌入到所有使用高速公路的汽车上。什么样的系统规模会改变你之前的分析。

PROBLEM B: College Coaching Legends

Sports Illustrated, a magazine for sports enthusiasts, is looking for the “best all time college coach” male or female for the previous century.Build a mathematical model to choose the best college coach or coaches(past or present)from among either male or female coaches in such sports as college hockey or field hockey, football, baseball or softball, basketball, or soccer.Does it make a difference which time line horizon that you use in your analysis, i.e., does coaching in 1913 differ from coaching in 2013? Clearly articulate your metrics for aement.Discu how your model can be applied in general acro both genders and all poible sports.Present your

model’s top 5 coaches in each of 3 different sports.In addition to the MCM format and requirements, prepare a 1-2 page article for Sports Illustrated that explains your results and includes a non-technical explanation of your mathematical model that sports fans will understand.体育画报，是一个为体育爱好者打造的杂志，它正在寻找上个世纪中男性或者女性的“全天候最好的大学教练”。建立一个数学模型，从，负责担任例如如下体育活动（高校曲棍球、场地曲棍球、足球、棒球、垒球、篮球、橄榄球）的男性或者女性教练中选择最佳大学教练或教练团体（过去或者现在的），在你的分析中在时间方面是否会造成一些不同，也就是说1913年的训练和2013年的训练有何不同。要求清楚的阐述你评估的指标。讨论你的模型是怎样应用在常见的两个性别都有的运动和全部可能的体育运动中。要求展示用你模型评估出的在3个不同运动中的前5名的教练。

除了MCM的格式和要求，为体育画报准备一份1-2页的文章，解释你的结果并包括能让您的体育爱好者都明白的、能有通俗易懂解释的数学模型。迷都明白的数学模型的非技术性解释。